Atkin-Lehner |
3+ 11- 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
80223f |
Isogeny class |
Conductor |
80223 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
270336 |
Modular degree for the optimal curve |
Δ |
-31408506320763 = -1 · 3 · 118 · 132 · 172 |
Discriminant |
Eigenvalues |
-2 3+ 0 1 11- 13+ 17+ -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-2218,273360] |
[a1,a2,a3,a4,a6] |
Generators |
[-75:110:1] [81:786:1] |
Generators of the group modulo torsion |
j |
-5632000/146523 |
j-invariant |
L |
5.1869187181774 |
L(r)(E,1)/r! |
Ω |
0.55166440454301 |
Real period |
R |
0.78352567784211 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000089 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
80223j1 |
Quadratic twists by: -11 |